Titlebar

Export bibliographic data
Literature by the same author
plus on the publication server
plus at Google Scholar

 

Exponential sensitivity analysis for Model Predictive Control of PDEs

URN to cite this document: urn:nbn:de:bvb:703-epub-4590-3

Title data

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Exponential sensitivity analysis for Model Predictive Control of PDEs.
Department of Mathematics, University of Bayreuth
Bayreuth , 2020 . - 4 S.

[img]
Format: PDF
Name: Sensitivity_preprint.pdf
Version: Published Version
Available under License Creative Commons BY 4.0: Attribution
Download (239kB)

Project information

Project title:
Project's official titleProject's id
Specialized Adaptive Algorithms for Model Predictive Control of PDEsGR 1569/17-1
Specialized Adaptive Algorithms for Model Predictive Control of PDEsSCHI 1379/5-1

Project financing: Deutsche Forschungsgemeinschaft

Abstract

Model Predictive Control (MPC) is a control method in which the solution of optimal control problems on infinite or indefinitely long horizons is split up into the successive solution of optimal control problems on relatively short finite time horizons. Only a first part of this solution with given length is implemented as a control for the longer, possibly infinite horizon. Motivated by this application, we analyze the propagation of discretization errors in the context of optimal control of abstract evolution equations in infinite dimensional spaces. Using a particular stability property, one can show that indeed the error decays exponentially in time, leading to very efficient time and space discretization schemes for MPC. In particular, one can rigorously explain the behavior of goal oriented error estimation algorithms used in this context. Furthermore, an exponential turnpike theorem will be derived. We give particular applications of this abstract theory to admissible control of hyperbolic equations, nonautonomous and semilinear parabolic equations. Eventually, we present several numerical examples illustrating the theoretical findings.

Further data

Item Type: Preprint, postprint
Keywords: Control of Distributed Parameter Systems; Optimal Control; Stability
Subject classification: Mathematics Subject Classification Code: 65M50, 49K40, 35Q93
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics > Chair Applied Mathematics - Univ.-Prof. Dr. Anton Schiela
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-4590-3
Date Deposited: 24 Jan 2020 06:36
Last Modified: 24 Jan 2020 06:36
URI: https://epub.uni-bayreuth.de/id/eprint/4590

Downloads

Downloads per month over past year